After speaking with a band director, a trumpet professor, and my trumpet teacher, we have decided that some of my issues could be solved with an embochure change. Here's what we considered: We'd like to shift the position of the mouthpiece more toward the center of the embochure and up to where more of the upper lip is inside the mouthpiece. In other words, we're going for a more centered mouthpiece.
What is the best way to change an embochure? Is there some kind of great process to it or what?